Question

Lg^2 x-3lg x-4=0 РЕШИТЕ СРОЧНО!

Answer 1

$lgx=-1$ или $lgx=4$
$x=10^{-1}$ или $x=10^4$
$x=\frac{1}{10}$ или $x=10000$
ответ: $\frac{1}{10}, 10000$

Answer 2

Solving the Equation lg^2(x) + lg(x) - 3lg(x) - 4 = 0

To solve the equation lg^2(x) + lg(x) - 3lg(x) - 4 = 0, we can use a substitution to simplify the equation. Let's denote lg(x) as a new variable, say y. Then the equation becomes a quadratic equation in terms of y.

So, the equation becomes: y^2 + y - 3y - 4 = 0

Simplifying this, we get: y^2 - 2y - 4 = 0

Now, we can solve this quadratic equation for y.

Solving the Quadratic Equation

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by: x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, the coefficients are: a = 1, b = -2, and c = -4

Substituting these values into the quadratic formula, we get: y = (2 ± √((-2)^2 - 4*1*(-4))) / (2*1) y = (2 ± √(4 + 16)) / 2 y = (2 ± √20) / 2 y = (2 ± 2√5) / 2 y = 1 ± √5

So, the solutions for y are: y = 1 + √5 and y = 1 - √5

Reverting to the Original Variable x

Now that we have the solutions for y, we can revert back to the original variable x using the substitution we made at the beginning.

Recall that we defined y as lg(x). Therefore, we have: lg(x) = 1 + √5 and lg(x) = 1 - √5

To solve for x, we need to exponentiate both sides using base 10, as lg (base 10 logarithm) is the logarithm with base 10.

Exponentiating both sides gives us: x = 10^(1 + √5) and x = 10^(1 - √5)

So, the solutions for the equation lg^2(x) + lg(x) - 3lg(x) - 4 = 0 are: x = 10^(1 + √5) and x = 10^(1 - √5)

These are the solutions for the given equation.